Question: Rewrite as a simplified fraction. ${1.1\overline{5} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 115.5555...\\ 10x &= 11.5555...\end{align*}}$ Subtracting the two equations, we have: ${90x = 104}$ ${x = \dfrac{104}{90}} $ ${x = \dfrac{52}{45}} \text{or} {1 \dfrac{7}{45}}$